Problem: Simplify the following expression: $\sqrt{63}+\sqrt{112}-\sqrt{175}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{63}+\sqrt{112}-\sqrt{175}$ $= \sqrt{9 \cdot 7}+\sqrt{16 \cdot 7}-\sqrt{25 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{7}+\sqrt{16} \cdot \sqrt{7}-\sqrt{25} \cdot \sqrt{7}$ $= 3\sqrt{7}+4\sqrt{7}-5\sqrt{7}$ Finally, simplify by combining the terms. $= ( 3 + 4 - 5 )\sqrt{7} = 2\sqrt{7}$